This work seeks to systematically model and solve the equations associated with the kinematics of spherical mechanisms. The group of special unitary matrices, SU(2), is utilized throughout. Elements of SU(2) are employed here to analyze the three-roll wrist and the spherical Watt I linkage. Additionally, the five orientation synthesis of a spherical four-bar mechanism is solved, and solutions are found for the eight orientation synthesis of the Watt I linkage. Using SU(2) readily allows for the use of a homotopy-continuation-based solver, in this case Bertini. The use of Bertini is motivated by its capacity to calculate every solution to a design problem.
Special Unitary Matrices in the Analysis and Synthesis of Spherical Linkages
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received April 14, 2018; final manuscript received September 21, 2018; published online November 13, 2018. Assoc. Editor: Hai-Jun Su.
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Almestiri, S. M., Murray, A. P., and Myszka, D. H. (November 13, 2018). "Special Unitary Matrices in the Analysis and Synthesis of Spherical Linkages." ASME. J. Mechanisms Robotics. February 2019; 11(1): 014503. https://doi.org/10.1115/1.4041633
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